m 


w 


re 


FIRST  YEAR  ALGEBRA  SCALES  series  a 

By  HENRY  G.  HOTZ 

Published  by  Teachers  College,  Columbia  University.  ^  Copyright,  1920,  by  Teachers  College 


School Date.- City „ County.. 

Write  your  name  here Age 

When  did  you  begin  to  study  algebra?    Month .....Year 


ADDITION  AND  SUBTRACTION 

Carefully  perform  the  operations  as  indicated. 


1.     4r  +  3r  +  2r  = 


3.     126  +  66-36 


5.     7x-x+6-4  = 


9.     (4r  -  5<)  +  (s  -  3r)  = 


10.     8c  -  ( -  6  +  3c)  = 


12,     5x  -  [4x  -  (3x  -  1)  ]  = 


^      3c       3c 
13. 

4        8 


15. 


3x 


a  —  X      c^  —  7? 


3  -  2a; 
18.     3 2x  = 


3  -  2x         X  +  1 
22. —^ 


{x  -  Vf      {x  -  \y      (x  -  1) 


23. 


20     +   x/"45"  +   yTVi 


24. 


a         a  -2  3 

a  -2     a+2      4:  -  a" 


577528 


FIRST  YEAR  ALGEBRA  SCALES*  '  series  a 

By  HENRY  G.  HOTZ 
Published  by  Teachers  College,   Columbia  University.     Copyright,  1920,  by  Teachers  College 

School Date City County 

Write  your  name  here Age 

When  did  you  begin  to  study  algebra?    Month Year 


MULTIPLICATION  AND  DIVISION 

Carefully  perform  the  operations  as  indicated.    Reduce  all  answers  to  their  simplest 
forms. 

12n 
\.    Z  .ly=  2.     —  = 

4 

3.    2a  .  4a62  =  7.    4x  .  (  -  Sxy^)  = 


ISmhi  -  27mn2 

9. »  11.    (2a2  +  7a  -  9)  (6a  -  1)  = 

9mn 


ci-d*       c-d 

16.     (  -  3x1/3)*  =  17.     .  

(c  -  d)2     c2  +  d2 


p2  _|_  4p  _  45      p8  _  8  1 

20. 


p2  +  2p  +  4      p2  _  81     3p,.  _  15^ 


x8  +  27           3x  +  9  2  1 

21.     4- 22.     64*  X  27*  = 

a;2  +  X  -  12         X  +  4 


3    V  6a 


23.    -—     .    V12a     = 

2aV  18 


c^ 


FIRST  YEAR  ALGEBRA  SCALES  series  a 

By  HENRY  G.  HOTZ 

Published  by  Teachers  College,  Columbia  University.     Copyright,  1920,  by  Teachers  College 

School Date City. County 

Write  your  name  here Age..._ 

When  did  you  begin  to  study  algebra?     Month Year._ 


EQUATION  AND  FORMULA 

Solve  the  following  equations  and  formulae: 
1.     2x  =  4.  2.     7m  =  3m  +  12. 

4.     5a  +  5  =  61  -  3a.  6.     10  -  llz  =  4  -  8z. 

8.     c  -  2(3  -  4c)  =  12. 


11.     The  area  of  a  triangle  =  ibh,  in  which 

b  =  length  of  the  base 

and  h  =  height  of  the  triangle. 

How  many  square  feet  are  there  in  the  area  of  a  triangle  whose  base  is  10  feet,  and 
whose  height  is  8  feet? 


X  +  3       X  +  5 
14.    3m  +  7n  =  34  18. 


7m  +Sn  =  46 


X  —  2      X  —  4. 


6x  -  2  3x»  +  13 

19.    p«  -  5p  =  50.  23.    — TT  ~  ^  =  ~1 — ^ 

^^  x  +  3  x'— 9 


24.     S  =  igt^;  solve  for  t.  25.     \/x»  -  1  -  x  =  -  1. 


Digitized  by  the  Internet  Archive 

in  2008  with  funding  from 

IVIicrosoft  Cbrporalid.n 


http://www.archive.org/detdrls/firstyearalgebraOOhotzrich 


FIRST  YEAR  ALGEBRA  SCALES  series  a 

By  HENRY  G.  HOTZ 
Published  by  Teachers   College,   Columbia   University.     Copyright,  1920,  by  Teachers  College 


School Date City County. 

Write  your  name  here Age 

When  did  you  begin  to  study  algebra?    Month Year 


PROBLEMS 

Do  not  work  out  the  answer  to  the  problem — merely  indicate  the  answer  or  state  the  equation 
in  each  case. 

1.    If  one  coat  cost  x  dollars,  how  much  will  3  coats  cost? 

Answer 1 ; ; 


2.    A  man  is  m  years  old;  how  old  was  he  r  years  ago?  „  ^ 

Answer 


4.     A  gold  watch  is  worth  ten  times  as  much  as  a  silver  watch,  and  both  together  are  worth  $132. 
How  much  is  each  worth? 


Equation. 


5.    The  distance  from  Chicago  to  New  York  by  rail  is  980  miles.     If  a  train  runs  v  miles  an  hour, 
what  is  the  time  required  for  the  run? 


Answer.. 


7.    The  total  number  of  circus  tickets  sold  was  836.     The  number  of  tickets  sold  to  adults  was  136 
less  than  twice  the  number  of  children's  tickets.     How  many  were  sold  of  each? 


Equation., 


8.  A  rectangular  box  is  d  inches  deep,  w  inches  wide,  and  contains  r  cubic  inches.     What  is 

its  length? 

Answer 

9.  The  area  of  a  square  is  equal  to  that  of  a  rectangle.    The  base  of  the  rectangle  is  12  feet 

longer  and  its  altitude  4  feet  shorter  than  the  side  of  the  square.     Find  the  dimensions 
of  both  figures. 


Equation 

(Turn  over.    There  are  problems  on  the  other  side) 


12.  A  train  leaves  a  station  and  travels  at  the  rate  of  40  miles  an  hour.  Two  hours  later  a 
second  train  leaves  the  same  station  and  travels  in  the  same  direction  at  the  rate  of  55 
miles  an  hour.     WTiere  will  the  second  train  pass  the  first? 


Equation.. 


13.  A  merchant  has  two  kinds  of  tea,  one  kind  costing  50  cents  and  the  other  65  cents  per  pound. 
How  many  pounds  of  each  must  be  mixed  together  to  produce  a  mixture  of  20  pounds 
that  shall  cost  60  cents  per  pound? 


Equation., 


14.    An  open  box  is  made  from  a  square  piece  of  tin  by  cutting  out  a  5-inch  square  from  each 

comer  and  turning  up  the  sides.    How  large  is  the  original 
I— T  square,  if  the  box  contains  180  cubic  inches? 

I 

Equation 


FIRST  YEAR  ALGEBRA  SCALES 

By  HENRY  G.  HOTZ 

Published  by  Teachers  College,  Columbia  University.    Copyright,  1820,  by  Teachers  College. 


SERIES  A 


School Date.. 

Write  your  name  here 


City _    County... 

- - Agt 


When  did  you  begin  to  study  algebra?   Month _   Year... 


GRAPHS 

1.      The  following  diagram  represents  the  length  of  certain  rivers: 


inssissippi 


ST-UViTajNCE 


YUKON 


ARKAMSAS 


COLUUBIA 


li  I  L  E  S 

How  many  miles  long  is  the  Arkansas  river  as  represented  in  this  diagram  ?.. 


3.      This  graph  indicates  the  population  of  a  certain  town  for  a  period  of  years : 


vasviATim 

3500 

A 

/ 

^ 

r     '" 

3400 

.^' 

^ 

y 

ssoo 

^ 

l^ 

3200 

1840 


1850 


YEAR 


1860 


What  was  the  approximate  population  of  the  town    in   1856?.. 


1870 


(Turn  ov(M') 


4.      This  table  gives  the  interest  at  6  per  cent  on  $100 
for  a  period  of  years: 


Years 

Interest 
in  Dollars 

1 

6 

2 

12 

3 

18 

4 

24 

5 

30 

6 

36 

Locate  in  the  adjacent  diagram  the  points  corresponding 
to  the  above  data. 

Then  connect  these  points  by  a  line. 


*'^'i 

30 

25  ■ 

hi 

Ul 

K 

W 

-i 

■ 

^  ^ 

tZ5 

— 1 

n 

io,__: 

J 

' 

" 

"■ 

~ 

~ 

~ 

~ 

^ 

^ 

"" 

^ 

■■ 

■■  ■" 

■ 

0  LLL 

^ 

^ 

^ 

„ 

^ 

^ 

^ 

^ 

^  ^ 

2       3       4        5       6 
Y  £  A  B  S 


5.      The  following  graph  is  used  to  convert  degrees  of  temperature  from  the  Fahrenheit  scale   (F)   to  the 
Centigrade  scale  (C)  and  from  the  Centigrade  scale  to  the  Fahrenheit  scale: 


Degrees 


F&hrenheit 


160- 

/ 

/ 

J 

ipfi. 

f 

/ 

1  no 

i 

f 

/ 

80 

> 

r 

/ 

60 

J 

f 

Af\- 

/ 

r 

on  ■ 

/ 

J 

r 

A< 

/ 

/ 

/ 

> 

/ 

_^ 

_ 

_ 

_ 

_ 

_ 

,^_ 

When  it  is  +20°  on  the  F  scale,  what  is  the  tem- 
perature in  degrees  on  the  G  scale? 


Degrees     Centigrade 


6.      This  graph  represents  the  distance  passed  over  by  a  man  walking  at  the  rate  of  3  miles  an  hour  for  a 
number  of  hours. 


30 


25 


20 

0} 
M 
►^  15 


10 


¥- H~i~" 

J  e 

7 

r 

J 

T 

L 

^d 

7 

r 

~/ 

7 

r 

"Ite" 

j_ 

f 

T 

7 

n^ 

jb 

7 

r 

T 

7 

r 

J 

7 

-J 

Z 

^      -                _        .      : 

0   2   4   6   8   lb  12  14  16  18  20  22 
H  0  U  B  S 


By  the  conditions  of  the  problem  it 
may  be  said  that  the  number  of  miles 
travelled  equals  three  times  the  num- 
ber of  hours,  or 

m  =  3  A 

That  is 

\i  h  =  2,  then  m  ^  6; 

if  /i  =  4,  then  m  ^  12; 
and  if  A  =  6,  then  m  =  18,  etc. 

By  locating  these  points,  we  have  a, 
b,  c,  d,  etc.,  of  the  graph. 


In  the  same  diagram  draw  a  graph 
in  which 

m  =  2h 


7.      Find  three  pairs  of  values  for  x  and  y  in  the  following  equation  and  then  draw  the  graph  of 


0 


X  +  y  =  5 


1  Space  =   1  Unit 


^     (TUTM    0V«C) 


10.       Plot  the  following  equations  and  find  the  values  of  x  and  y  at  the  point  of  intersection  of  the  graphs. 


y 

~~  0  


I  +  4y  =  11 
2x  —    y  =    4 


1  Space  =   1  Unit 


11.      A  boy  begins  work  with  a  weekly  wage  of  $9  and  receives  an  increase  of  25  cents  every  week.    Another 

boy  starts  with  a  weekly  wage  of  only  $6,  but  re- 
ceives an  increase  of  50  cents  every  week. 


1 

Draw  a  graph  which  shows  the  wage  of  each  at 
the  beginning  of  every  week  for  15  weeks. 

According  to  this  graph  when  will  their  wages 
be  the  same  ? 


FIRST  YEAR  ALGEBRA  SCALES  series  b 

By  HENRY  G.  HOTZ 

Published  by  Teachers  College,  Columbia  University.     Copyright,  1920,  by  Teachers  College 

School Date.- City. County._ 

Write  your  name  here Age : 

WTien  did  you  begin  to  study  algebra?    Month Year.„ 


ADDITION  AND  SUBTRACTION 

Carefully  perform  the  operations  as  indicated. 

1.     4r  +  3r  +  2r  =  2.     2x  +  3a;  = 

3.     126  +  66  -  36  =  4.     2c  +  §c  = 

5.     7a-  -  a-  +  6  -  4  =  6.     3a  -  46  +  5a  -  26  = 

7.     5m  +  (  -4to)  =  8.     20a;  -  (10a;  +  5a;)  = 


9.     (4r  -  5t)  +  (*  -  3r)  =  10.     8c  -  (  -  6  +  3c)  = 


11,     3a2  -  36  -  (2a2  +  36  -  4)  =  12.     bx  -  [Ax  -  (3x  -  1)  ] 


3c        3c                                                                   3a;  —  2          a;  +  4 
13. =  14. \ 

4         8  3  6 


(Turn  over.     There  are  exercises  on  the  other  side) . 


3x 


15. 


a  —  X        (fi  —  x^ 


r               r 
16.    — \ 

r  +  z       r  — 


17. 


oa  +  1       3a  -  2 


6a  2a 


3  -  2x 
18.     3 2x 


19. 


lOx  +  Sy       3x  +  5y 


2xhf  xy^ 


a  a  —  4 


20. 


a  +  1      a2-a  +  l       a3+l 


15 


21. 


x2  -  5x  +  6       x2  +  2x  -  15 


3  -  2a:          a;  +  1                 1 
22.    + 


ix  -  1)3  (x  -  1)2  {x   -   1) 


23.     V  20  +    V  45  +    V    ^,  = 


24. 


a  -  2  3 

+ 


a  -  2  a  +  2        4-a2 


FIRST  YEAR  ALGEBRA  SCALES  series  b 

By  HENRY  G.  HOTZ 
Published  by  Teachers  College,  Columbia  University.     Copyright,  1920,  by  Teachers  College 

School ...Date.-. City. County. 

Write  your  name  here Age 

When  did  you  begin  to  study  algebra?    Month Year 


MULTIPLICATION  AND  DIVISION 

Carefully  perform  the  operations  as  indicated.     Reduce  all  answers  to  their  simplest 
forms. 

12n 

I.    3  •  7y  =  2.    = 

4 

3.     2a  .  4a62  =  4.     6c3  ^  2c2  = 


5.     I  of  9??i  = 


8a% 


4a2 
7.     Ax  '  (-  3xy^)  =  8.     a3  .  (-  3a)  •  (-  2a) 


18^%  —  21mrfl                                                    Ax^ 
9.     ^  10.     H-  2a;2  = 


9mn  5 


n4  +  7n2  -  30 

11.     (2a2  +  7a  -  9)  (5a  -  1)  =  12.     

n2  -  3 


7a       7a2  -  I2x2y2  .   (x  -  2) 

13.     —  -^  —  =  14.     

15       20  -  3x2^/2 


(Turn  over.     There  are  exercises  on  the  other  side) 


15. 


m  -\-  n 


a 


m^  —  7j2 


16.     (  -  3x2/3)4  = 


17. 


d'^      c  -  d 


{C   -  d)2      c2  +  ^2 


1  3 

18.      3x2    .   43-2 


19. 


a2  +  2  "  ~  1 
a  +  2 


20. 


p2  +  4p  —  43      p3  _  3 


p2  +  2p  +  4       p2  -  81       Spr  -  15r 


21. 


x3  +  27 


3x  +  9 


x2  +  X  -  12         X  +  4 


2  1 

22.     643  X  273  = 


3  V   6a  

23.    ^—  .    V  12a  = 

2a  V  18 


c^Ts  ^  t:::c3Uxcc«-«-«-^->*-«-«-  ''";:5 


FIRST  YEAR  ALGEBRA  SCALES  series  b 

By  HENRY  G.  HOTZ 
Published  by  Teachers  College,  Columbia  University.     Copyright,  1920,  by  Teachers  College 


School Date City..  County- 
Write  your  name  here Age... 

When  did  you  begin  to  study  algebra?    Month ...Year 


EQUATION  AND  FORMULA 

Solve  the  following  equations  and  formulae: 
1.     2x  =  4.  2.     7m  =  3m  +  12. 

3.     3.r  +  3  =  9.  4.     5a  +  5  =  61  -  3a. 

5.     7»  -  12  -  3n  +  4  =  0.  6.     10  -  llz  =  4  -  82. 

7.     |z  =  6.  8.     c  -  2(3  -  4c)  =  12. 


2x        5 
i.r  +  i.r  =  3.  10.     —  =  — 

3         8 


11.     The  area  of  a  triangle  =  ^bh,  in  which 

b  =  length  of  the  base 
and  h  =  height  of  the  triangle. 
How  many  square  feet  are  there  in  the  area  of  a  triangle  whose  base  is  10  feet,  and 
whose  height  is  8  feet? 


y         5         y 

12.     —  = —  .  13.     Kx-  +  5)  =  5. 

3         2         4 


(Turn  over.    There  are  exercises  on  the  other  side) 


14.     3m  +  7n  =  34  15.    =  

7m  +  8n  =  46  3  -  a;        1  +  x 

16.  The  area  of  a  circle  =  ttt^,  in  which 

r  =  radius  of  the  circle 
and  TT  =  3| 

Find  the  area  in  square  feet  of  circle  whose  radius  is  7  feet. 

17.  In  the  formula  RM  =  El,  find  value  of  M. 


X  +  3        X  +  5 

18. = 19.     p^  -  5p  =  50. 

X  —  2        X  —  4 


2  3  12 

20.    = 21.    —  +  —  =  1 

x2  +  4x  +  3     a;2  +  3x  +  2  x         y 

4         4 
X        y 


22.    F  =  temperature  in  Fahrenheit  degrees 
C  =  temperature  in  Centigrade  degrees 
9C 

andF  = h  32°. 

5 
Solve  for  C  when  F  =  70°. 


6x  -  2  3x2  +  13 

23. 3  =  

X  +  3  x2  -  9 

24.  S  =  ^gfi;  solve  for  t. 

25.  V  x2  -  1  -  X  =  -  1. 


0,\  V.  R^JTY  OF  CALIFORNIA 
BtRKELEY.  CAUIFOkinIm, 


SERIES  B 


FIRST  YEAR  ALGEBRA  SCALES 

Hems  G.  Hotz 

School Date City - County.. 

Write  your  name  here _ Age 

When  did  you  begin  to  study  algebra  ?    Month Year _. 


PROBLEMS 

Do  not  work  out  the  answer  to  the  problem  —  merely  indicate  the  answer  or  stale  the  equation  in  each  case. 

I .     If  one  coat  cost  x  dollars,  how  much  will  3  coats  cost  > 

Answer _ _ 


2.     A  man  is  m  years  old;  how  old  was  he  r  years  ago? 

Answer. 


3.     A  boy  has  a  marbles  and  buys  b  more;  how  many  has  he  then? 

Answer 


4.  A  gold  watch  is  worth  ten  limes  as  much  as  a  silver  watch,  and  both  together  are  worth  $132.   How  much  is  each  worth? 

Elquation _ : - 

5.  The  distance  from  Chicago  to  New  York  by  rail  is  980  miles.    If  a  train  runs  v  miles  an  hour,  what  is  the  time  required 

for  the  run  ? 

Answer 


6.     The  width  of  a  basket  ball  court  is  20  feet  less  than  its  length.    The  perimeter  of  the  court  (distance  around)  is  240 
feet.    Find  the  dimensions. 


Equation.. 


7.     The  total  number  of  circus  rickets  sole'  was  836.     The  number  of  tickets  sold  to  adults  was  1 36  less  than  twice  the 
number  of  children's  rickets.    How  many  were  sold  of  each? 


Equarioo.. 


(Turn  over.    There  are  problems  on  the  other  side) 


8.     A  rectangular  box  is  d  inches  deep,  w  inches  wide,  and  contains  r  cubic  inches.    What  is  its  length  > 

Answer 


9.     The  area  of  a  square  is  equal  to  that  of  a  rectangle.     The  base  of  the  rectangle  is  12  feet  longer  and  its  altitude 
4  feet  shorter  than  the  side  of  the  square.     Find  the  dimensions  of  both  figures. 

Equation 

1 0.     A  tower  casts  a  shadow  of  20  feet.     A  man.  5  feet  9  inches  high,  who  is  near  at  the  same  time,  casts  a  shadow 
of  2  feet  6  inches.    Find  the  height  of  the  tower. 

Proportion 


1 1 .     Five  thousand  dollars  is  invested  in  two  banks,  part  in  one  at  3  per  cent  and  the  rest  in  the  other  at  4  per  cent 
The  annual  income  from  die  two  investments  is  $172.     How  much  is  each  investment? 


Equation. 


12.     A  train  leaves  a  station  and  travels  at  the  rate  of  40  miles  an  hour.    Two  hours  later  a  second  train  leaves  the  same 
station  and  travels  in  the  same  direction  at  the  rate  of  55  miles  an  hour.    Where  will  the  second  train  pass  the  first? 


Equation- 


1 3.     A  merchant  has  two  kinds  of  tea,  one  kind  costing  50  cents  and  the  other  65  cents  per  pound.    How  many  pounds  of 
each  must  be  mixed  together  to  produce  a  mixture  of  20  pounds  that  shall  cost  60  cents  per  pound? 


Equation.- 


14.     An  open  box  is  made  from  a  square  piece  of  tin  by  cutting  out  a  5  inch  square  from  each  comer  and  turning  up  the 

sides.    How  large  is  the  original  square,  if  the  box  contains  180  cubic  inches? 


I  ^^»  Equation.. 


PUBUSHEO  BY 
TEACHERS    COLLEGE,   COLUIIBIA    UNIVEBSITY 
COmUGHT,     1920,     BY     TEACHEBS     COIXEGE 


r.t 


r 


LANOe  LIBRARY  OF  EDUCATtnw 

UMV^RSITY  OF  CAUFOR^N^'f  "* 
BERKELEY.  CALIFORNIA 


FIRST  YEAR  ALGEBRA  SCALES  series  a 

By  HENRY  G.  HOTZ 

Published  by  Teachers  College,  Columbia  University.     Copyright,  1920,  by  Teachers  College 


School Date City County- 
Write  your  name  here Age 

When  did  you  begin  to  study  algebra?     Month._ Year 


ADDITION  AND  SUBTRACTION 

Carefully  perform  the  operations  as  indicated. 


1.     4r+3r  +  2r  = 


3.     126  +  66  -  36  = 


5.     7a;-x+6-4  = 


9.     (4r  -  50  +  (s  -  3r)  = 


10.     8c  -  ( -  6  +  3c)  = 


12.     5x  -[4x  -  (3x  -  1)  ]  = 


..      3c       3c 
13. = 

4       8 


15. 


Sx 


a  —  X     a?  —  x^ 


18.    3 2x  = 


22. 


3  -  2x         X  +  1 


{x  -  \y    {x  -  \y    (x  - 1) 


23.     ^r^  +  a/Is"  +  vOi" 


a         a  -2  3 

24. r-  +  ■ 


a  -2     a +2      4-0^ 


• 


577528 

L 


UNIVERSITY  OF  CALIFORNIA  UBRARY 


^mmmmm^' 


